Finite Group Databasebeta

← C2×#10589339 #11796337

Subgroups — C2×#10589339 #11796337

Order 1152.

852 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64145C211yesmaximal, characteristic
2C2×C32×#99C211yesmaximal, characteristic
3C2×#63661C211yesmaximal, characteristic
4#10589339C214yesmaximal, direct product factor
5C2×#4473—34nomaximal
6C22×C32×D4C2211yescharacteristic
7C22×#634C411yescharacteristic, complemented
8C2×C32×C22⋊C4—21no—
9C2×#3757—21no—
10C2×#3757—21no—
11C2×#3757—21no—
12#64145—21no—
13#64145—21no—
14#64145C412yescomplemented
15#64145C2212yes—
16C2×C4×C3⋊Dic3C411yescharacteristic, complemented
17C32×#99—21no—
18C32×#99C2212yes—
19#63661—21no—
20#63661C2212yes—
21C2×#936—34no—
22C2×C3×#99D314yes—
23C2×#834—34no—
24#4473—316no—
25C24×C32D411yescharacteristic
26C24×C32D411yescharacteristic
27C2×C32×D4—41no—
28C2×C32×D4—41no—
29C2×C32×D4C2×C411yescharacteristic
30C2×C32×D4D411yescharacteristic
31C2×C32×D4D411yescharacteristic
32C2×C32×D4C2311yescharacteristic
33C22×C32×C4—41no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—41no—
38C2×#634—21no—
39C2×#634—41no—
40C2×#634—41no—
41C2×#634C2×C412yescomplemented
42C32×C22⋊C4—22no—
43C32×C22⋊C4—41no—
44#3757—22no—
45#3757—22no—
46#3757—22no—
47#3757—22no—
48#3757—22no—
49#3757—41no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3C2×C412yescomplemented
52C2×#354—91noSylow
53C22×C3×D4C2×D314yes—
54C22×Dic6—34no—
55C2×C3×C22⋊C4—24no—
56C2×#217—64no—
57C2×#217—64no—
58C2×#217—64no—
59#936—38no—
60#936—38no—
61#936—64no—
62#936—64no—
63C2×C4×Dic3—34no—
64C3×#99—24no—
65C3×#99C2×D318yes—
66#834—38no—
67#834—64no—
68C23×C32—21no—
69C23×C32—21no—
70C23×C32—21no—
71C23×C32—21no—
72C23×C32—42no—
73C23×C32—42no—
74C23×C32C22⋊C411yescharacteristic
75C23×C32C22⋊C411yescharacteristic
76C23×C32C22⋊C411yescharacteristic
77C23×C32C2×D411yescharacteristic
78C23×C32C2×D411yescharacteristic
79C32×D4—41no—
80C32×D4—41no—
81C32×D4—41no—
82C32×D4—41no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—42no—
86C2×C32×C4—82no—
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C22×C411yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—42no—
95C2×C3⋊Dic3—82no—
96#634—42no—
97#634—42no—
98C2×#124—91no—
99C2×#99—91no—
100C2×#99C3⋊D311yescharacteristic
101#354—94no—
102C24×C3D1214yes—
103C24×C3#6714yes—
104C2×C3×D4—44no—
105C2×C3×D4—44no—
106C2×C3×D4C4×D314yes—
107C2×C3×D4D1214yes—
108C2×C3×D4#6714yes—
109C2×C3×D4C22×D314yes—
110C22×C3×C4—44no—
111C22×C3×C4C4×D314yes—
112C22×Dic3—64no—
113C22×Dic3—64no—
114C22×Dic3—124no—
115C2×Dic6—38no—
116C2×Dic6—64no—
117C2×Dic6—124no—
118C2×Dic6—124no—
119C3×C22⋊C4—28no—
120C3×C22⋊C4—44no—
121#217—68no—
122#217—68no—
123#217—68no—
124#217—68no—
125#217—68no—
126#217—124no—
127C4×Dic3—38no—
128C4×Dic3—64no—
129C22×C32—22no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—41no—
135C22×C32—41no—
136C22×C32—41no—
137C22×C32—41no—
138C22×C32—42no—
139C22×C32—42no—
140C22×C32—81no—
141C22×C32—81no—
142C22×C32#9911yescharacteristic
143C22×C32#9911yescharacteristic
144C22×C32C2×C22⋊C411yescharacteristic
145C32×C4—21no—
146C32×C4—21no—
147C32×C4—82no—
148C3⋊Dic3—42no—
149C3⋊Dic3—42no—
150C3⋊Dic3—82no—
151C22×Q8—91no—
152C22×D4C2×C3⋊D311yescharacteristic
153#124—92no—
154#124—92no—
155#124—181no—
156#124—181no—
157C2×C22⋊C4—21no—
158C2×C22⋊C4—181no—
159C2×C22⋊C4—181no—
160C2×C22⋊C4—181no—
161C2×C42—91no—
162#99—21no—
163#99—92no—
164#99—181no—
165#99C2×C3⋊D312yes—
166C23×C3—24no—
167C23×C3—24no—
168C23×C3—24no—
169C23×C3—24no—
170C23×C3—48no—
171C23×C3—48no—
172C23×C3(C2×D3)⋊C414yes—
173C23×C3(C2×D3)⋊C414yes—
174C23×C3(C2×D3)⋊C414yes—
175C23×C3C2×D1214yes—
176C23×C3C2×#6714yes—
177C3×D4—44no—
178C3×D4—44no—
179C3×D4—44no—
180C3×D4—44no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—48no—
184C2×C3×C4—88no—
185C2×C3×C4(C2×D3)⋊C414yes—
186C2×C3×C4C2×C4×D314yes—
187C2×Dic3—68no—
188C2×Dic3—68no—
189C2×Dic3—128no—
190C2×Dic3—124no—
191C2×Dic3—124no—
192C2×Dic3—128no—
193C2×Dic3—248no—
194Dic6—128no—
195Dic6—128no—
196C2×C32—21no—
197C2×C32—21no—
198C2×C32—41no—
199C2×C32—41no—
200C2×C32—41no—
201C2×C32—41no—
202C2×C32#35412yescomplemented
203C2×C32C2×#9911yescharacteristic
204C24C4⋊(C3⋊D3)11yescharacteristic
205C24#63811yescharacteristic
206C2×Q8—92no—
207C2×Q8—181no—
208C2×Q8—361no—
209C2×Q8—361no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4C4×C3⋊D311yescharacteristic
213C2×D4C4⋊(C3⋊D3)11yescharacteristic
214C2×D4#63811yescharacteristic
215C2×D4C22×C3⋊D311yescharacteristic
216C22×C4—41no—
217C22×C4—181no—
218C22×C4—181no—
219C22×C4—361no—
220C22×C4C4×C3⋊D311yescharacteristic
221C22⋊C4—22no—
222C22⋊C4—41no—
223C22⋊C4—182no—
224C22⋊C4—182no—
225C22⋊C4—182no—
226C22⋊C4—182no—
227C22⋊C4—182no—
228C22⋊C4—361no—
229C42—92no—
230C42—181no—
231C22×C3—28no—
232C22×C3—24no—
233C22×C3—24no—
234C22×C3—24no—
235C22×C3—24no—
236C22×C3—44no—
237C22×C3—44no—
238C22×C3—44no—
239C22×C3—44no—
240C22×C3—48no—
241C22×C3—48no—
242C22×C3—84no—
243C22×C3—84no—
244C22×C3#80614yes—
245C22×C3#80614yes—
246C22×C3C2×(C2×D3)⋊C414yes—
247C3×C4—24no—
248C3×C4—24no—
249C3×C4—88no—
250Dic3—128no—
251Dic3—128no—
252Dic3—248no—
253C32C2×#35411yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—42no—
259C23—42no—
260C23#375211yescharacteristic
261C23#375211yescharacteristic
262C23#375211yescharacteristic
263C23C2×C4⋊(C3⋊D3)11yescharacteristic
264C23C2×#63811yescharacteristic
265Q8—362no—
266Q8—362no—
267D4—41no—
268D4—41no—
269D4—41no—
270D4—41no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—362no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4—362no—
281C2×C4—722no—
282C2×C4#375211yescharacteristic
283C2×C4C2×C4×C3⋊D311yescharacteristic
284C2×C3—24no—
285C2×C3—24no—
286C2×C3—44no—
287C2×C3—44no—
288C2×C3—44no—
289C2×C3—44no—
290C2×C3#447318yescomplemented
291C2×C3C2×#80614yes—
292C22—22no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—81no—
305C22#6363311yescharacteristic
306C22#6363311yescharacteristic
307C22C2×#375211yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—362no—
312C4—362no—
313C4—722no—
314C3C2×#447314yescomplemented
315C2—21no—
316C2—21no—
317C2—41no—
318C2—41no—
319C2—41no—
320C2—41no—
321C2#1058933912yesdirect product factor
322C2C2×#6363311yescharacteristic
subgroupG/H
centerC22#63633
commutatorC2×C32×C4C22×C4
FrattiniC2×D4C22×C3⋊D3
FittingC2×C32×#99C2
socleC22×C32#99
prime radicalC22×C32×D4C22
cosocleC2×C32×D4C23
hypercenterC2×#99C3⋊D3
hypocenterC32C2×#354
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #10589339C2direct (N × H)
7. C22×#634C4semidirect
14. #64145C4semidirect
16. C2×C4×C3⋊Dic3C4semidirect
41. C2×#634C2×C4semidirect
51. C4×C3⋊Dic3C2×C4semidirect
202. C2×C32#354semidirect
253. C32C2×#354semidirect
290. C2×C3#4473semidirect
314. C3C2×#4473semidirect
321. C2#10589339direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#641452
C2×C32×#992
C2×#636612
#105893392
C2×#44733